Splitting Tensile Force in Rectangular Plates Fixed Along One Side and Loaded at the Opposite Side

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Splitting Tensile Force in Rectangular Plates Fixed Along One Side and

Loaded at the Opposite Side

Hiltscher, R.; Florin, G.

https://publications-cnrc.canada.ca/fra/droits

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PREFACE

The Division of Building Research has been interested in precast concrete construction in general for a number of years and more recently has been lnvolved in an active research programme on the connections between precast structural members. One of the more fundamental problems in this area is the bearing capacity of

concrete plates under

a

concentrated load, as for instance in the

head of a column carrying one or more beams.

The results of the Swedish studies presented in this paper (one of a series by the same authors) contribute greatly to an understanding of the stress distribution and of the mechanism involved in the failure of concrete subjected to such loads. This translation is therefore provided to make this Information more readily available to designers and others involved in the field of precast concrete.

The Division is indebted to one of its own members,

W.R.

Schriever, Head of the Building Structures Section for this trane- lation.

Ottawa

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Title:

NATIONAL RESEARCH COUNCIL OF CANADA Technical Translation 1224

The splitting tensile force in rectangular plates fixed along one side and loaded at the opposite side

( ~ i e Spaltzugkraft In einseitig eingespannten, am

gegenuberliegenden Rande belasteten rechteckigen ~cheiben) Authors : R. Hiltscher and G. Florin

Reference: Bautechnik,

39

(10): 325-328, 1962

Translator: W.R. Schriever, Division of Building Research, National Reseamh Council

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THE SPLITTING TENSILE FORCE I N RECTANGULAR PLATES FIXED A M N G ONE SIDE AND LOADED AT THE OPPOSITE SIDE

A b s t r a c t

The problem of t h e d i s t r i b u t i o n o f s p l i t t i n g t e n s i l e s t r e s s e s i n a p l a t e under l o a d , a problem which s o f a r h a s been solved r i g o r o u s l y o n l y f o r a load on a n i n f i n i t e l y l o n g s t r i p , i s s t u d i e d by photo- e l a s t i c model methods f o r a p l a t e of f i n i t e dimension which i s f i x e d a l o n g one s i d e and loaded a t t h e o t h e r s i d e by a r e l a t i v e l y concen- t r a t e d symmetrical load ( a s f o r i n s t a n c e a c o n c r e t e w a l l on r o c k o r a f m n d a t i o n w i t h t h e load of a beam o r heavy machines, on t o p , e t c . ) .

The b a s i s f o r a n a c c u r a t e d e s i g n of t h e r e i n f o r c i n g a g a i n s t t h e s p l i t t i n g f o r c e s r e s u l t i n g from such a load i s g i v e n i n t h e form o f a diagram f o r t h e r e s u l t a n t s p l i t t i n g t e n s i l e f o r c e and i t s l o c a t i o n a s a f u n c t i o n of t h e p l a t e h e i g h t and t h e load c o n c e n t r a t i o n r e l a - t i v e t o t h e p l a t e w i d t h .

I.. I n t r o d u c t i o n

It h a s been known f o r a l o n g t i m e t h a t under a l o a d which a c t s o n

w a l l - l i k e p l a t e , t e n s i l e s t r e s s e s a r e produced which l e a d t o s p l i t t i n g c r a c k s i n t h e p l a t e ( F i g . 1 ) . Morsch and B l e i c h d e r i v e d t h e f i r s t c a l c u l a t i o n me- t h o d s f o r t h i s c a s e . It i s o n l y w i t h t h e advent of p r e s t r e s s e d c o n c r e t e , i n which problems of r e i n f o r c i n g such danger zones under t h e anchor b l o c k s a r o s e , t h a t t h e s o l u t i o n of t h i s q u e s t i o n became u r g e n t . Approximate s o l u t i o n s were produced i n r a p i d s u c c e s s i o n by ~ u ~ o n ( l ) , S i e v e r s , Magnel and Ban. I y e n g a r (2) f i n a l l y d e r i v e d a n e x a c t s o l u t i o n f o r t h e i n f i n i t e l y l o n g h a l f - s t r i p loaded on i t s narrow s i d e . If t h e t y p e of problem a r i s e s i n which t h e s p l i t t i n g f o r c e i n a c o n c r e t e w a l l under t h e i n f l u e n c e of a heavy load c o n c e n t r a t e d on a s m a l l d i s t a n c e must be c a l c u l a t e d , t h e n t h e s o l u t i o n f o r t h e i n f i n i t e l y l o n g h a l f - s t r i p i s n o t s u f f i c i e n t . A w a l l u s u a l l y i s of r a t h e r l i m i t e d h e i g h t and i s , i n g e n e r a l , f i x e d on t h e o p p o s i t e s i d e i n t h e f o u n d a t i o n o r on r o c k . T h i e f i x a t i o n u s u a l l y r e s u l t s i n a c o n s i d e r a b l e r e d u c t i o n o f t h e s p l i t t i n g e f f e c t . S i n c e t h e problem j u s t d e s c r i b e d d o e s n o t l e n d i t s e l f e a s i l y t o a r i g o r o u s

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1

s o l u t i o n , p h o t o s t r e s s model measurements were r e s o r t e d t o a t a n e a r l y s t a g e . The development i n t h a t l a s t few y e a r s of p h o t o s t r e s s methods u s i a l a t e r a l

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extensometer and p o l a r i s c o p e l e d t o a procedure o f h i g h a c c u r a c y which now o f f e r s , when used w i t h a s u f f i c i e n t number of models f o r t h e t e s t s , t h e b a s i s f o r a g e n e r a l and e x a c t e x p e r i m e n t a l s o l u t i o n of t h e problem.

2 . T e s t P l a n n i n q

F i g u r e 1 shows a b a s i c s k e t c h of t h e model i n v e s t i g a t e d w i t h t h e terms ueed. The e l a s t i c p l a t e i s f i x e d a l o n g i t s bottom s i d e i n t o a n e l a s t i c semi-

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i n f i n i t e body of t h e same modulus a s t h e p l a t e , corresponding t o t h e f i x a t i o n of a c o n c r e t e w a l l In rock o r i n a f o u n d a t i o n b l o c k . I n t h e model t h i s f i x a - t i o n was achieved by g l u i n g t h e 10 mm t h i c k model p l a t e made of A r a l d i t i n a s u f f i c i e n t l y l a r g e block of t h e same m a t e r i a l . The width of t h e load was t h e same f o r a l l t e s t s , t h a t i s , a = 12 mm. T h i s load width, a , r e p r e s e n t s t h e b a s i c measure f o r t h e p r e s e n t a t i o n of t h e s t r e s s d i s t r i b u t i o n under t h e l o a d . The l a t e r a l s t r e s s ox ( F i g . 1) which i s of i n t e r e s t h e r e , i s a compressive

s t r e s s d i r e c t l y under t h e l o a d , but changes, a t a d i s t a n c e roughly e q u a l t o t h e width of t h e l o a d , t o a t e n s i l e s t r e s s a s a r e s u l t of t h e s p r e a d i n g of t h e c o n c e n t r a t e d load over t h e width of t h e p l a t e . T h i s t e n s i l e s t P e s s r e a c h e s a maximum and f i n a l l y d i m i n i s h e s t o 0 f a r t h e r from t h e l o a d , a t a d i s t a n c e a t which t h e s t r e s s d i s t r i b u t i o n h a s reached i t s f i n a l form ( p a r a l l e l s t r e s s l i n e s ) . The s p l i t t i n g e f f e c t which r e s u l t s from t h i s s t r e s s d i s t r i b u t i o n can be c h a r a c t e r i z e d by t h e r e s u l t i n g s p l i t t i n g t e n s i l e f o r c e H which h a s a d i s - t a n c e from t h e loaded edge of yH.

The t e n s i l e s t r e s s e s ox depend mainly on two parameters:

( a ) The r e l a t i v e load width a/b, o r t h e i n v e r s e v a l u e b/a, which i s c a l l e d t h e "load c o n c e n t r a t i o n f a c t o r " . For t h e load d i s t r i b u t e d uniformly over t h e p l a t e width, 1 . e . f o r a load c o n c e n t r a t i o n f a c t o r b/a = 1, no t e n s i l e s t r e s s occurred under t h e l o a d . For t h e o t h e r extreme c a s e , however, b/a = m,

t h e s p l i t t i n g e f f e c t r e a c h e s a maximum a s y m p t o t i c a l l y .

( b ) The r e l a t i v e p l a t e h e i g h t h/b. T h i s determines t h e r e d u c t i o n of t h e s p l i t t i n g e f f e c t f o r s m a l l e r p l a t e h e i g h t s d u e t o t h e e f f e c t of f i x a t i o n along t h e lower edge, and v a r i e s between h/b = 0 and h/b = 3:00. The l a t t e r value i s t h e l i m i t i n g c a s e f o r t h e i n f i n i t e l y high h a l f - s t r i p a c c o r d i n g t o I y e n g a r .

I n o r d e r t o produce a f u l l s o l u t i o n t o t h e problmm t h e parameters b/a and h/b must be v a r i e d i n t h e model t e s t s between t h e l i m i t s i n d i c a t e d above, w i t h t h e " i n f i n i t e " v a l u e s being reproduced by s u f f i c i e n t l y l a r g e v a l u e s , because of t h e asymptotic c o n d i t i o n of t h e s p l i t t i n g e f f e c t . The t e s t s e r i e s were arranged i n such a way t h a t f i r s t t h e b a s i c models w i t h r e l a t i v e h e i g h t s of h/a =

5,

h/a

=lo,

and h/a = 23 were made. The load c o n c e n t r a t i o n f a c t o r b/a was produced by stepwise r e d u c t i o n of t h e p l a t e width t o v a l u e s b/a = 29, 16, 1 2 , 8 and

4.

An a d d i t i o n a l t e s t w i t h a s t i l l lower model with a r e l a t i v e p l a t e h e i g h t of h/b = 0.2 was a l s o made, s o t h a t t h e f u l l i n v e s t i g a t i o n aov- ered 1 6 d i f f e r e n t models.

I n p r a c t i c e , a c c u r a t e s t r e s s d i s t r i b u t i o n under t h e load i s u s u a l l y not w e l l known. I n planning t e s t s i t i s t h e r e f o r e n e c e s s a r y t o d e c i d e w i t h which load d i s t r i b u t i o n t h e i n v e s t i g a t i o n s h a l l be made. I n F i g . 2 some t y p i c a l c a s e s a r e shown. A s e r i e s of p r e l i m i n a r y t e s t s showed t h a t t h e r e s u l t i n g s p l i t t i n g t e n s i l e f o r c e i n t h e c a s e of a r a t h e r r i g i d l o a d i n g body ( F i g . 2 a )

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i s approximately 1 0 p e r c e n t s m a l l e r , and I n t h e c a s e of a c y l i n d r i c a l l o a d i n g body ( ~ i g . 2 c ) , r e s u l t i n g i n a n e l l i p t i c a l s t r e s s d i s t r i b u t i o n because of a h i g h e r load c o n c e n t r a t i o n , approximately 10 p e r c e n t g r e a t e r t h a n f o r t h e r e l a - t i v e l y r a r e c a s e of a u n i f o r m l y d i s t r i b u t e d l o a d ( F i g . 2 b ) . The f a c t t h a t t h e d i f f e r e n c e s a r e s o s m a l l can be e x p l a i n e d by s t a t i n g t h a t t h e c h a r a c t e r i s t i c p r e s s u r e d i s t r i b u t i o n under t h e l o a d s p r e a d s o u t r a p i d l y a c c o r d i n g t o t h e p r i n c i p l e of S t . Venant. S i n c e t e n s i l e s t r e s s e s o c c u r o n l y a t a c e r t a i n d i s - t a n c e from t h e edge of t h e p l a t e ( ~ l g . l ) , t h e d i f f e r e n c e s i n t h e l o a d d i s t r i -

b u t i o n a t t h e s u r f a c e i s of s m a l l s i g n i f i c a n c e f o r them. The model t e s t s were t h e r e f o r e c a r r i e d o u t o n l y f o r a u n l f o r m l y d i s t r i b u t e d l o a d . A c o r r e s p o n d i n g c o r r e c t i o n can be made f o r p o s s i b l e o t h e r known l o a d d i s t r i b u t i o n s .

The f a c t t h a t s p l i t t i n g t e n s i l e s t r e s s e s o c c u r o n l y a t a c e r t a i n d i s t a n c e below t h e loaded edge i s v e r y f a v o u r a b l e f o r measurement w i t h a l a t e r a l e x t e n -

someter. S i n c e t h e l a t e r a l s t r a i n I n t h e immediate v i c i n i t y of t h e a p p l i e d l o a d i s r e s t r a i n e d , a t h r e e - d i m e n s i o n a l s t a t e o f s t r e s s o c c u r s t h e r e which malces measurements w i t h a l a t e r a l extensometer q u e s t i o n a b l e . Measurements con- c e r n i n g t h i s ( 6 ) have, however, ahown t h a t even under a l o a d i n g body which i s

glued on ( i n t h e p r e s e n t c a s e t h e l o a d wao o n l y s e t o n ) , t h e e f f e c t on t h e l a t - e r a l extensometer measurement a t a d i s t a n c e of 2

-

3a from t h e u p p e r edge was o n l y 1

-

2 p e r c e n t . Concerning t h e a p p l i c a t i o n of t h e model r e s u l t s t o t h e f u l l s i z e p r o t o - t y p e , i t must be s t a t e d f i r s t t h a t t h e s t r e s s d i s t r i b u t i o n i n t h e p r e s e n t two d i m e n s i o n a l c a s e i s independent of t h e l a t e r a l c o n t r a c t i o n c o e f f i c i e n t and n a t u r a l l y a l s o of t h e e l a s t i c modulus of t h e m a t e r i a l . The r e s u l t s of t h e model t e s t s , p r e s e n t e d i n d i m e n s i o n l e s s form, a r e t h e r e f o r e d i r e c t l y a p p l i c a - b l e t o any o t h e r e l a s t i c m a t e r i a l . I n o r d e r t o p r e s e r v e g e o m e t r i c s i m i l a r i t y between t h e model ( M ) and t h e p r o t o t y p e ( H ) i n t h e loaded c o n d i t i o n , t h e s t r a i n s must be t h e same i n b o t h c a s e s :

The same r e l a t i o n s h i p i s a l s o v a l i d f o r t h e mean l o a d i n t e n s i t y Q = P/a.t (where t i s t h e t h i c k n e s s of t h e p l a t e ) which a l s o h a s t h e u n i t of a s t r e s s ,

whereby q/E i s c a l l e d t h o r e l a t i v e l o a d i n t e n s i t y . For c o n c r e t e w i t h

9 = a b = 100 k d s q cm and Eb = 300,000 k d s q cm we o b t a i n q / ~ = o .33 10".

whereas one would p r e f e r f o r p h o t o s t r e s s methods t o have a l o a d i n t e n s i t y a s h i g h a s p o s s i b l e i n o r d e r t o produced s t r e s s e s and s t r a i n s which a r e e a s y t o measure. I n o r d e r t o d e t e r m i n e t o what e x t e n t one may d e v i a t e I n t h e p r e s e n t

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s t u d y was made w i t h f o u r d i f f e r e n t l o a d s on t h e same model. The r e s u l t s a r e shown on F i g . 3. I t can be seen from t h i s t h a t a r e l a t i v e load i n t e n s i t y of

2

.

i . e . a s i x - f o l d i n c r e a s e 1s s t i l l j u s t a c c e p t a b l e . F i g u r e 3 i n c i - d e n t a l l y g i v e s a n i d e a of t h e r e l i a b i l i t y of t h e p h o t o s t r e s s measurements by means of t h e p o l a r i s c o p e and l a t e r a l extensometer.

3. T e s t s and E v a l u a t i o n

I n t h e main t e s t s t h e s t r e s s e s ax a l o n g t h e a x i s of symmetry and, t o check t h e e q u i l i b r i u m c o n d i t i o n s , t h e s t r e s s e s a i n any chosen h o r i z o n t a l

Y

s e c t i o n were determined f o r 1 6 model v a r i a t i o n s a s i n d i c a t e d above by meas- u r i n g t h e p r i n c i p a l s t r e s s sums and d i f f e r e n c e s (6-8)

.

F i g u r e s 4-6 show, f o r f i f t e e n of t h e i n v e s t i g a t e d c a s e s , t h e d i s t r i b u t i o n of t h e s p l i t t i n g t e n s i l e s t r e s s ox i n d i m e n s i o n l e s s form w i t h t h e r e f e r e n c e s t r e s s q =

at.

From t h e s e c u r v e s t h e r e s u l t i n g s p l i t t i n g t e n s i l e f o r c e H/P and i t s r e l a t i v e d i s - t a n c e from t h e loaded edge yH/a was determined by t a b l e i n t e g r a t i o n . These two v a l u e s , which i n each c a s e e s s e n t i a l l y d e s c r i b e t h e s p l i t t i n g e f f e c t , a r e p l o t t e d i n F i g . 7 a s f u n c t i o n s of t h e load c o n c e n t r a t i o n f a c t o r b/a and t h e r e l a t i v e p l a t e h e i g h t h/b.

4 . R e s u l t s

From t h e two diagrams i n F i g . 7 i t f o l l o w s t h a t :

1. For t h e l o a d uniformly d i s t r i b u t e d o v e r t h e l e n g t h of t h e p l a t e , w i t h a l o a d c o n c e n t r a t i o n f a c t o r of b/a = 1, t h e s p l i t t i n g t e n s i l e f o r c e i s 0 .

2 . With i n c r e a s i n g load c o n c e n t r a t i o n b/a t h e s p l i t t i n g t e n s i l e f o r c e i n - c r e a s e s and r e a c h e s a p r a c t i c a l l i m i t i n g v a l u e f o r b / a > 3 0 , From t h e t e n s i l e s t r e s s d L s t r i b u t i o n obtained by ~ y e n ~ a r ' ~ ) f o r t h e l i m i t i n g c a s e of b/a = m and h/b = co i t can be c a l c u l a t e d i n a n approximate way t h a t f o r b/a = 30 approximately 90% of t h e l i m i t i n g v a l u e h a s been reached, and t h a t H/P = 0 . 3 ( a p p r o x i m a t e l y ) r e p r e s e n t s a n upper l i m i t i n g v a l u e of t h e s p l i t t i n g t e n s i l e f o r c e .

3. F i x a t i o n a l o n g t h e lower p l a t e edge r e s u l t s i n a r e d u c t i o n of t h e s p l i t - t i n g t e n s i l e f o r c e . With r e l a t i v e p l a t e h e i g h t i n c r e a s i n g from h/b = 0 t o h/b = m ( c a s e a c c o r d i n g t o I y e n g a r ) t h e s p l i t t i n g t e n s i l e f o r c e i n - c r e a s e s from 0 t o a maximum v a l u e . The maximum i s a l r e a d y p r a c t i c a l l y reached f o r p l a t e s w i t h a r e l a t i v e h e i g h t of h/b = 2 t o 3. For p l a t e s w i t h a g r e a t e r h e i g h t t h a t h/b = 2 (approximately) t h e i n f l u e n c e o f t h e f i x a t i o n a l o n g t h e lower edge i s no l o n g e r of any p r a c t i c a l s i g n i f i c a n c e .

4. The r e s u l t a n t of t h e s p l i t t i n g t e n s i l e f o r c e o c c u r s i n g e n e r a l a t a d i s - t a n c e of 2 - ha below t h e loaded edge. With i n c r e a s i n g load c o n c e n t r a t i o n

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b/a and with increasing relative slab height h/b the depth of the resultant increases also.

5.

Considerations for the Design of the Reinforcing

The resultant splitting tensile force H/P and its location below the

loaded edge yH/a can be read from the diagrams in Fig.

7

for each case. A

steel reinforcement area calculated in this way, and related to the line of force given in the diagram would balance the splitting tensile force. This, however, does not yet guarantee that no tensile stresses will occur and that there is absolute assurance against cracking. If all tensile stresses are to be avoided, then the reinforcernent has to be distributed according to the ac-

curate stress distribution in the diagrams of Fig. 4

-

6,

as long as this ap-

pears at all worthwhile considering the small tensile stresses.

It should be noted here that it is not necessary to carry out model testa

with the reinforcement according to the method given in reference 9 . In the

present case the reinforcement, designed properly for value and position, ia positioned such that it will have its maximum efficiency. In contrast to this

in reference

9

_{the problem of the tear tensile force of a loaded corner has}

been studied, whereby a saving up to

60%

can be achieved by moving the rein-

forcement from the centre towards the edge of the plate, The solution of this statically indeterminate problem has so far only been achieved in model tests with reinforced models.

If one wants to apply a correction for the deviation of load distribution from the case of a uniformly distributed load, for which the tests were made, one should, as already mentioned in Section 2, first determine clearly what the actual load distribution is. The case of the rigid body and that of a uniformly distributed load will be rather rare in practice, as will the special

case of a cylindrical body with an elliptical load pressure distribution (wheel on a rail). Load distributions in the form of a bell-shaped curve under only moderately thick plates, such as shown for instance in Fig. 2d, will, however, be quite frequent. The concentration of the load intensity towards the line of symmetry is in this case even higher than for the case of the elliptical pressure distribution. Since, however, the accurate load distribution is known only very rarely, and since,furthermore, it is rarely possible to develop a splitting tensile stress diagram for each load distribution, the estimated load distribution is replaced by a corresponding elliptical dis-

tribution with the reduced width a', approximately as shown in Fig. 2d (45'

distribution), for which distribution a correction of +lo$ compared to the case of the uniformly distributed load is known. From the diagram for the splitting tensile force one can see furthermore whether or not the present

(9)

On the basis of similar conolderations it should be possible, by means of the splitting tensile diagram for a plate, to obtain at least an estimate of the splitting tensile effect for three-dimensional problems such as for the

case of a real load on a crane runway on a concrete wall.

In conclusion the authors wish to thank Tor Hafstad for the conscientious execution of the tests.

References

--

1. Guyon, Y. Contraintes dans les pikces prismatiques soumises

B

des forces

appliquees sur leurs bases, au voislnage de ces bases (stresses in

priv~natic bodies subJected to forces on their bases near these bases).

Abh. Int. Vereinig. f. Brflcken- und Hochbau, 11: 165-226, 1951.

2. Sundara Raja lyengar, K .T

.

Der Spannungszustand in einem elastischen

Halbstreifen und seine tcchnischen Anwendugen

an he

state of stress

in an elastic semi-strip and its technical applications). PhD thesis,

Technical University of Hannover, 1960.

3.

Nylander, H. and Holst, H. Nagra undersijlcningar rorande skivor och hoga

balkar av armerad betong. Kungl. T e h . Hdgskolans handlingar Nr. 2,

Stockholm, 1946.

4.

Christodoulides, S . P

.

A two-dimensional investigation of the end anchor-

age of post-tensioned concrete beams. Struct. Englr. 120-132, 1955.

5.

Christodoulides, S.P. A photoelastic investigation of prestressed concrete

anchorage. Civil Engineering and Public Works Review, 51:994-997, 1956.

6.

Hiltscher, R. Development of the lateral extensometer method in two-

dimensional photoelasticity. Int. Symp. on Photoelasticity, Chicago, 1961.

7.

Hiltscher, R. Abschnitt Spannungsoptik in: Handbuch der Spannungs- und

Dehnungsmessung (chapter on photostress methods in the handbook of stress and constant measurement). K. Fink and Christian Rohrbach. Dusseldorf 1958.

8.

Miiller, R.K. Erfahrungen mit dem Lateralextensometer (Experience with

the lateral extensometer). Bautechnik, 38:

364-368,

1961.

9.

Hiltscher, R. and Mfiller, R.K. Bemessung der Bewehrung von Stahlbeton-

konstruktionen mit Hilfe des spannungsoptischen Modellversuches

(~esign of the reinforcing of reinforced concrete constructions by

(10)

Fig. 1

Diagrammatic sketch and nomenclature

Pig. 2

Different load distributions

(a) Pressure of a rigid body on a soft semi-infinite body; (b) Arrangement for

the production of a nearly truly uniformly distributed load; (c) Elliptical load dl-tribution under a cylindrical body; (d) Load distribution under a base plate of a structural section. This distribution can be replaced in practice

(11)

Dependence of t h e s p l i t t i n g t e n s i l e f o r o e on t h e r e l a t i v e l o a d i n t e n s i t y i n t h e model t e s t dslq o ooz aot Fig. 4 S p l i t t i n g t e n s i l e s t r e s s e s ox/q as

a

f u n c t i o n of t h e d i s t a n c e y/a from t h e loaded edge f o r

v a r i o u s load c o n c e n t r a t i o n s b/a f o r a c o n s t a n t model h e i g h t h/b =

5

(12)

Splitting tensile stresses ax/q a8

a

function of the distance y/a from the loaded edge for various

load concentrations b/a for a constant model height of h/a = 10

Splitting tensile stresses ox/q as a function of the distance y/a from the loaded edge for various load concentrations b/a for a constant model height of h/a =

(13)

The r e l a t i v e s p l i t t i n g t e n s i l e f o r c e H/P and i t s p o s i t i o n yr/a as f u n c t i o n s of

t h e load c o n c e n t r a t i o n b/a and t h e r e l a t i v e p l a t e h e i g h t h/b